Problem: Simplify the following expression: $k = \dfrac{5a^2 - 5a - 280}{a + 7} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $5$ , so we can rewrite the expression: $ k =\dfrac{5(a^2 - 1a - 56)}{a + 7} $ Then we factor the remaining polynomial: $a^2 {-1}a {-56} $ ${7} {-8} = {-1}$ ${7} \times {-8} = {-56}$ $ (a + {7}) (a {-8}) $ This gives us a factored expression: $\dfrac{5(a + {7}) (a {-8})}{a + 7}$ We can divide the numerator and denominator by $(a - 7)$ on condition that $a \neq -7$ Therefore $k = 5(a - 8); a \neq -7$